Two-agent scheduling on bounded parallel-batching machines with an aging effect of job-position-dependent
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Two‑agent scheduling on bounded parallel‑batching machines with an aging effect of job‑position‑dependent Jun Pei1,2,3 · Jinling Wei1 · Baoyu Liao1,2 · Xinbao Liu1,2 · Panos M. Pardalos3
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract This paper investigates a competitive two-agent parallel-batching scheduling problem with aging effect on parallel machines. The objective is to minimize the makespan of agent A with the constraint that the makespan of agent B is no more than a given threshold. Some key structural properties are first identified in two different cases, and based on these structural properties a novel decision tree of scheduling rules is constructed and a heuristic algorithm is designed. Then, an effective hybrid BF-VNS algorithm combining Bacterial Foraging (BF) with variable neighborhood search (VNS) is developed to tackle the studied problem. Computational experiments are conducted to evaluate the performance of the proposed hybrid algorithm and some other well-known algorithms. The experimental results indicate that the hybrid BF-VNS algorithm performs quite better than the compared algorithms. Keywords Scheduling · Two-agent · Parallel-batching · Aging effect · Bacterial Foraging · Variable neighborhood search
1 Introduction The batch scheduling problems exist in many practical manufacturing environments, such as continuous casting (Liu et al. 2010b) and hot rolling process (Liu et al. 2010a) in the steel industry, recrystallization process in aircraft engine industry (Wang et al. 2017), transportation process in two-level supply chain (Yin et al. 2016), and some platform enterprises (Diakité et al. 2012). The processing way of the batch scheduling problems can lead to improving in productivity in such manufacturing industries, where the * Jun Pei [email protected] * Xinbao Liu [email protected] 1
School of Management, Hefei University of Technology, Hefei, China
2
Key Laboratory of Process Optimization and Intelligent Decision-making of Ministry of Education, Hefei, China
3
Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA
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Vol.:(0123456789)
Annals of Operations Research
two-agent scheduling may exist due to the interest conflicts of different agents. In this paper, a competitive two-agent scheduling problem on parallel-batching machines is investigated, featured by aging effect and compatible jobs, position-dependent processing times and bounded machine capacity. This problem is motivated by the processes of aluminummaking in an aluminum plant as shown in Fig. 1. All the semi-finished aluminum products are put into the aging furnace for processing. After this process finished, some finishedaluminum products are outsourced to a partner, and others are continuously processed in the aluminum manufacturer, which can be deemed to two agents for the jobs in the aging furnace. The semi-finished aluminum products are regarded as jobs scheduled sequentially. An aging furnace i
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